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Thursday, March 12, 2009

Black holes and decoherence

The black hole information problem (Wikipedia entry) is considered one of the deepest puzzles in theoretical physics. It is a "respectable" area of research with connections to string theory, quantum gravity and quantum information theory. In contrast, quantum foundations -- for example, the measurement problem (see, e.g., the Wikipedia or Stanford encyclopedia of philosophy entry) -- is considered a fringe activity by many working physicists. I've never understood this perspective, unless one claims that quantum foundations are somehow not testable experimentally and therefore more properly in the domain of philosophy. In our paper we argue that experiments relevant to black hole information are actually harder than those which address foundational questions in quantum mechanics. In fact, both types of experiments hinge on the ability to detect or manipulate macroscopic superpositions -- i.e., Schrodinger's Cat states. If the measurement problem and wavefunction collapse belong in the realm of philosophy, then so does the black hole information problem.

As John Bell said, "I am a Quantum Engineer, but on Sundays I have principles"! Bell famously hid his interest in quantum foundations for many years, afraid of the opprobrium of his colleagues at CERN and elsewhere. The first question he would ask of others who approached him about research on such topics was "Do you have a permanent job?" Bell's Theorem has been called "the most profound discovery of science."

For people interested in this subject, some recommended reading.

Against 'Measurement' by J.S. Bell. This paper originated from a lecture he gave in Erice at the summer school (Ettore Majorana) in 1989. I was a student there just the following year, so I narrowly missed meeting him in person, something I will always regret! Bell's discussion of measurement following that of K. Gottfried (pp. 35-38; when does the pure state become a mixture?) is closest to the formulation in our paper.

A book of essays in honor of Bell: Quantum [Un]speakables, edited by R. Bertlmann and A. Zeilinger, which contains fascinating material about his intellectual development, the Bell inequalities, their theoretical origins and experimental tests.

We investigate the experimental capabilities required to test whether black holes destroy information. We show that an experiment capable of illuminating the information puzzle must necessarily be able to detect or manipulate macroscopic superpositions (i.e., Everett branches). Hence, it could also address the fundamental question of decoherence versus wavefunction collapse.

"David H. Wolpert, a physics-trained computer scientist at the NASA Ames Research Center, has chimed in with his version of a knowledge limit. Because of it, he concludes, the universe lies beyond the grasp of any intellect, no matter how powerful, that could exist within the universe. Specifically, during the past two years, he has been refining a proof that no matter what laws of physics govern a universe, there are inevitably facts about the universe that its inhabitants cannot learn by experiment or predict with a computation. Philippe M. Binder, a physicist at the University of Hawaii at Hilo, suggests that the theory implies researchers seeking unified laws cannot hope for anything better than a “theory of almost everything.”

Yes, I should have recommended Bell's own essays, although they reveal less about the social pressure he had to overcome to pursue his "hobby" :-)

I am in total agreement with Bell on the need to think things through carefully, not just FAPP, but our opinions on Bohmian mechanics and Everett are exactly reversed! Bohm was useful to Bell as an explicit counterexample to the faulty von Neumann "proof" of no hidden variables. Bell also was very interested in models of fundamental collapse, which I think have not gotten much attention and (if correct) could interfere with the proper functioning of quantum computers.

To answer your question: yes, it appears that fighting decoherence is the toughest part of doing a bh information experiment!

In retrospect, it is obvious: Hawking claimed bh's could make a pure state evolve to a mixed state. But decoherence does this all the time, FAPP. To tell whether it is caused by the bh rather than decoherence, one needs to turn off (defeat) the latter. One has to go beyond FAPP!

I thought a bit once about the collapse models and their impact on quantum computing. It wasn't clear to me what they do to quantum computing. On the one hand, a theory like the GRW theory basically has random stochastic localizations, which I think quantum error correction should be able to correct. On the other hand the GRW modification, if I recall correctly, makes quantum theory nonlinear, which almost always leads to move powerful computational models for quantum computers.

Re: GRW and fundamental collapse, yes they might ultimately yield *more* powerful models of computation, but they probably make a mess of your favorite (reversible) algorithm composed only of unitaries!